Stochastic Network Equilibrium with Multiple Vehicle Types and Asymmetric, Indefinite Link Cost Jacobians

Abstract

This paper discusses a family of general link cost functions that can be used to model multimodal transportation network equilibrium problems. The family includes as a special case the currently favored family of monotonically increasing functions but does not necessarily have to have a symmetric or semi-definite Jacobian. In this way multimodal networks can be modeled somewhat more realistically. The paper also allows stochastic link costs for some or all the links and modes. It is shown that under mild conditions the equilibrium exists and is unique, but more importantly, that there is a simple, single-equilibrium algorithm that is proven to converge for stochastic networks with the link cost family discussed in the paper. Finally, it is pointed out that many variable demand problems also exhibit unique equilibria, but that there are some which do not. An example which illustrates this fact is given.

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